Even-odd entanglement in boson and spin systems

Abstract

We examine the entanglement entropy of the even half of a translationally invariant finite chain or lattice in its ground state. This entropy measures the entanglement between the even and odd halves (each forming a "comb" of $n/2$ sites) and can be expected to be extensive for short range couplings away from criticality. We first consider bosonic systems with quadratic couplings, where analytic expressions for arbitrary dimensions can be provided. The bosonic treatment is then applied to finite spin chains and arrays by means of the random phase approximation. Results for first neighbor anisotropic XY couplings indicate that while at strong magnetic fields this entropy is strictly extensive, at weak fields important deviations arise, stemming from parity-breaking effects and the presence of a factorizing field (in which vicinity it becomes size-independent and identical to the entropy of a contiguous half). Exact numerical results for small spin s chains are shown to be in agreement with the bosonic RPA prediction.

10 pages, 4 figures

References in corpus (10)

• Unitarily localizable entanglement of Gaussian states
• Divergence of the entanglement range in low dimensional quantum systems
• Theory of ground state factorization in quantum cooperative systems
• Separability and ground state factorization in quantum spin systems
• Entanglement of finite cyclic chains at factorizing fields
• Two-spin entanglement distribution near factorized states
• Genuine multipartite entanglement of symmmetric Gaussian states: Strong monogamy, unitary localization, scaling behavior, and molecular sharing structure
• Comb entanglement in quantum spin chains
• Evaluation of ground state entanglement in spin systems with the random phase approximation
• Evaluation of pairwise entanglement in translationally invariant systems with the random phase approximation